The value is=?

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Answer 1 · 2018-06-26T10:09:27

The Right Option is #(4) : (5sqrt6)/12#.

Let, #a,b in RR^+" such that, "a > b#.

Their #"AM"=(a+b)/2," and the GM"=sqrt(ab)#.

It is given that, #(a+b)/2=5sqrt(ab)#.

#:. (a+b)=10sqrt(ab)#.

#:. (a+b)^2=100ab........................(ast^1)#.

Further, #(a-b)^2=(a+b)^2-4ab#.

#=100ab-4ab..........[because, (ast^1)]#.

#:. (a-b)^2=96ab..............................(ast^2)#.

From #(ast^1) and (ast^2)#, we have,

#(a+b)^2/(a-b)^2=(100ab)/(96ab)=25/24#.

#:. (a+b)/(a-b)=+sqrt(5^2/(2^2*6))............[because, (a-b) gt 0]#,

#=5/(2sqrt6)*sqrt6/sqrt6#.

# rArr (a+b)/(a-b)=(5sqrt6)/12#, showing that,

The Right Option is #(4) : (5sqrt6)/12#.